74.13.14 problem 31

Internal problem ID [16380]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.5, page 175
Problem number : 31
Date solved : Tuesday, January 28, 2025 at 09:07:21 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+7 y^{\prime \prime \prime }+6 y^{\prime \prime }-32 y^{\prime }-32 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 26

dsolve(diff(y(t),t$4)+7*diff(y(t),t$3)+6*diff(y(t),t$2)-32*diff(y(t),t)-32*y(t)=0,y(t), singsol=all)
 

\[ y = \left (c_{2} {\mathrm e}^{6 t}+c_{1} {\mathrm e}^{3 t}+t c_4 +c_{3} \right ) {\mathrm e}^{-4 t} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 34

DSolve[D[y[t],{t,4}]+7*D[ y[t],{t,3}]+6*D[y[t],{t,2}]-32*D[y[t],t]-32*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-4 t} \left (c_2 t+c_3 e^{3 t}+c_4 e^{6 t}+c_1\right ) \]